D-Plane Golf

This is the 2nd post in my instructional series on the golf swing. If this is your first time here, I suggest starting from the beginning, as these posts are in sequential order and build on each other.

Throughout the post, you may see small superscripts like this one 1)This is a superscript. Hover over the superscript to see additional commentary.

The D-Plane..

Is this a swing theory?

Who came up with it?

Why should anyone care?

In short, this was a theory which originated in the book The Physics of Golf by Theodore Jorgensen, and later popularized by Trackman Golf. The “D-Plane” is an extension of our “new ball flight laws” which provides a more comprehensive model for understanding spin and ball flight. In the previous post, I covered the basics of ball flight, while in this post, I will be getting into additional factors such as why the ball rises, and how weather conditions affect ball-flight.

Since this previous post covered the absolute basics of ball-flight, I suggest taking a glance at that before reading this post. Most golfers will find that this previous post of mine is sufficient for them in understanding the flight of the golf ball. That being said, it doesn’t even begin to cover ALL the factors that affect ball-flight. As a recap, we established the following 12 factors affecting the flight of the ball:

Club-face angle

Club-path angle

Relationship between sole of club and ground at impact (lie angle)

Point of contact on the face of the club

Angle of attack

Dynamic Loft

Velocity of club-head (at beginning and end of impact)

Mass of club-head

Quality of contact

Wind

Temperature

Elevation difference between start point and end point

In this post, I will be explaining the factors in bold through the lens of the “D-Plane” concept, and then move on to the remaining factors.

Essentially, the D-Plane is a model for understanding the starting direction, spin axis, and lift that the ball experiences thanks to the dimpled design of modern golf balls. The main difference between understanding the D-Plane and understanding the basic club-face angle to club-path angle is the fact that the D-Plane includes a vertical club-path vector in it as well. I have not yet explained the horizontal and vertical club path vectors, so you may want to read the first half of my post about the inclined plane in conjunction with this one, as they complement each other.

The D-Plane also takes into account the dynamic loft of the club at impact, which is also a fairly new concept.

In summary, the D-Plane involves the following factors:

Club-path angle

Club-face angle

Dynamic loft

Angle of Attack

The Venturi Effect (derived from Bernoulli’s Equation, also known as “lift”)

The D-Plane

Since I have already covered the concepts of club path angle and club face angle, I will not be going into detail here. As a reminder..

Club Face Angle: “the horizontal orientation of the club face at the center-point of contact between the club and ball at the time of maximum compression”

Club Path Angle: “the horizontal movement of the club head’s geometric center at the time of maximum compression”

Now, for the new concepts:

Dynamic Loft

Definition: “the vertical orientation of the club face at the center-point of contact between the club and the ball at the time of maximum compression.”

Simply put, the dynamic loft is represented by a perpendicular vector to the club-face at impact. On drivers and fairway woods, the faces have a slight convex shape to them, which means that the dynamic loft will be increased/decreased when struck high or low on the face. As you may infer, the dynamic loft is largely responsible for the initial trajectory of the golf shot.

Angle of Attack

This concept is fairly difficult to understand without a clear concept of the inclined plane, so if it becomes blurry at any point, review the inclined plane post.

Definition: “The vertical movement of the club head’s geometric center at the time of maximum compression”

Lift and Drag

Out of all the components in the D-Plane, this is arguably the most difficult concept to wrap your head around. If you do not feel like thinking deeply at the moment, just remember that a) the golf ball will rise when it has backspin, and b) the golf ball will curve in the direction of its spin axis tilt.

For the curious golfers out there, bare with me while I attempt to explain fluid dynamics in a few short paragraphs.

In order to do this, lets start by asking the question, “What is air?”

Although it doesn’t sound natural to say it, air is considered a “fluid,” and thus follows the laws set out by Bernoulli’s Principle. In short, this equation explains the inverse relationship between the speed of a fluid and the pressure of the fluid.

“In steady flow, the sum of all forms of energy in a fluid along a streamline is the same along all points in that streamline.” In other words, when a fluid is forced through a smaller area, it inherently increases its flow speed to conserve momentum, and experiences a smaller static pressure (conservation of momentum). In addition, fluids tend to flow from an area of high pressure to an area of low pressure.

If you don’t believe me, take two sheets of paper, and hold them vertically next to each other. Now blow between the two sheets. Contrary to your intuition, the sheets of paper will come together. This is because you have increased the speed of the air between them, thus lowering the static pressure of the fluid between the sheets. The pressure of the air on the outside of the sheets is not moving, which means it has higher pressure, and therefore will push in on the sheets of paper.

Knowing all this, we have a better chance of understanding why the golf ball flies as far as it does (often in the wrong direction for most golfers).

Consider the diagram below:

In the picture above, I have drawn a golf ball and the visual representation of air in the form of little lines. The longer lines represent air moving at a faster speed, and this image is from a “side-on” view of the golf ball.

The ball is traveling leftward in the image, which causes “drag.” You know that feeling when you stick your hand out the window of your car on the highway? That’s drag.

What is happening is the air at the front-center of the ball is stopping completely, causing an area of high pressure. The air that doesn’t stop at the front-center will move at a higher speed around the ball, and will continue in a tangential path to the top and bottom of the ball as indicated in area “A” and “B.” Although most of the air flows in that tangential direction, a thin layer breaks off in a “wake” behind the ball (area “C”), which is an area of low pressure.

So not accounting for spin yet, we have established that the front of the ball experiences high pressure, while the back of the ball experiences low pressure. Fluids move from high to low pressure, therefore, there is a “drag” force pushing against the golf ball.

Now, consider what happens when the ball is spinning.

When the ball spins, the rough surface of the golf ball (thanks to the dimples) grabs hold of a layer of air (red dashes), and drags it in a clockwise direction (the direction of the spin). Since the air is moving rightward as a result of drag, that layer of air (caused by the dimples and spin) will be moving faster in region A (because it is moving in the same direction as the air), and moving slower at the bottom of the ball (region B). Once again, fluids move from high pressure to low pressure, and thus the ball is “lifted” as a result of the dimples and spin. In addition to this lift, the ball still experiences drag as a result of the high pressure at the front of the ball compared to the low pressure at the back of the ball.

Finally, consider what happens when the spin axis is tilted in either direction. The drag force is still the same, but now, the areas of low/high pressure caused by the dimples and spin are favoring one side of the ball, and therefore the ball experiences “lift” in a sideways direction.

So what is the D-Plane??

We have finally defined all the components of the D-Plane, so explaining the concept will not be all that difficult.

Essentially, the D-Plane is a triangular plane that is formed by joining two straight lines:

Line 1: The directional line the club is moving at time of maximum compression

Line 2: The directional line perpendicular to the club face

Let’s start with the first line, which is actually the combination of club path angle and angle of attack. In my post about the inclined plane, I talk about how the club has both a horizontal and vertical directional vector. With some simple vector addition, we can derive this “sum” vector that represents the first line of our D-Plane, and combines the horizontal and vertical components of motion together.

For the second line, we are again looking at the combination of two components. No vector addition is necessary, because we can explain this second line using a magnetic lie angle tool. Not only does this lie angle tool show us the dynamic loft at impact, but it also shows us the club-face angle at impact.

Now that we have derived both lines, all we have to do is join them in a single inclined plane:

The D-Plane is just a fancy way of explaining the “new ball flight laws” and the venturi effect all in one. The initial starting direction of the ball is on a line within the D-Plane slightly below the perpendicular line (dynamic loft/face angle), and “lift” (as explained in the Venturi effect) causes the ball to move “up-plane” towards the line representing dynamic loft.

It is a useful model because of how intuitive it is.

If you tilt the D-Plane, the spin axis is tilted, and the ball curves.

If you increase the angle between line #1 (the sum vector of club path angle and angle of attack) and line #2 (the dynamic loft/club face angle), you increase the amount of spin. This will all start to feel more “applicable” after reading the next two posts in the instructional series.

Other Ball-Flight Factors

Through the concept of the D-Plane, we can understand how the first 6 factors on our list affect the flight of the ball, but our understanding is still incomplete. In this section, I will be explaining the remaining factors, which are comprised of:

Velocity of clubhead (at beginning and end of impact)

Mass of clubhead

Quality of contact

Wind

Temperature

Golf Ball (coefficient of restitution)

Elevation difference between start point and end point

To maintain the collective sanity of golfers, I won’t be getting too technical here, but will be covering the essentials that should provide practical benefit to any golf game.

Velocity of the Club-head

This one is simple. Ceteris Paribus, increasing the velocity of the clubhead is going to increase both the drag and spin imparted on the golf ball during flight. This means that the ball will experience more lift and will curve further offline when the spin axis is tilted in either direction.

Practical conclusions?

Golfers with higher swing speeds will benefit greatly from a proper club-fitting, which will allow the golfer to reduce the high spin rates which factory shafts inherently create. Those who do not swing as fast should not worry as much about a fitting, but would still benefit from one.

When it is windy, swinging faster is the kiss of death. Learn how to hit a knock-down shot with a bigger club!

Mass of the Club-Head

This factor is slightly different than the previous. All things equal, increasing the mass of the club-head increases the spin, drag, and lift on the ball, but only to a certain extent. After reaching a certain weight, the increases in distance will plateau.

Conclusions?

Generally, there is no point in adding large amounts of weight to the clubhead. The only useful benefit of adding weight to the club head is for a better “feel” see my post on swing-weight

Quality of Contact

Note: Although striking the ball “off-center” described as the “gear effect” would technically count as “poor quality” of contact, I will not be considering it under this section. Here I will be assuming that the golfer has made center contact, but not clean contact.

It isn’t rocket science. If you catch a bunch of turf between the club face and the ball, the ball isn’t going to fly very far, and it won’t have much spin. Although this is self explanatory, there is one factor that is worth talking about. This is called the “flyer.”

The “flyer” happens when the golfer has made solid contact, but there is a very thin layer of grass between the club-face and the ball. Normally, the ball stays in one spot on the club-face during the entire impact interval, and the spin is caused by the divergence between the two lines that we discussed in the D-Plane. When there is a thin layer of grass between the club-face and the ball, the ball will actually slide up the face slightly, and will lose a significant amount of spin. Although this results in less “lift,” these shots tend to travel further than usual (less drag), especially with the short-mid irons.

Identifying a “flyer lie” is often difficult to do, but in general, you will get flyers when the ball is sitting up, the grass is medium length rough, and the grass is pointing towards the target. In the end, it is a guessing game, and even the best pros will suffer from distance control out of the rough because of this.

The conclusion?

Hit the fairway.

Wind

Now, we are getting into the factors out of our direct control. As we all know, wind can be quite menacing during a round of golf, and there are a few key things to understand in order to play in the wind successfully.

First and foremost, let’s look back at the Venturi effect that we derived earlier in this post. What causes “lift” is the differing pressures above and below the golf ball during flight. When you add wind to the equation, these pressure differentials increase and decrease depending on the type of wind.

A shot hit with a perfectly level spin axis will have more lift into a headwind, and less lift into a tailwind.

By understanding this, it is clear that when playing into the wind, a straight ball (level spin axis) will tend to balloon straight up in the air while draws and fades will turn into hooks and slices respectively. When playing down-wind, a straight ball will struggle to get up into the air, while draws and fades will tend to become straighter shots.

I know this may not surprise anyone, but playing intothe wind is MUCH HARDER than playing down-wind. I don’t think it takes fluid mechanics to explain this simple fact of golf.

The question really becomes: “How do we play better in the wind?”

To play better in the wind, we must do two things.

Decrease spin rates and launch angles

Estimate distances correctly

Decreasing spin rates on all your shots is simple, yet most golfers struggle with this. Unfortunately, controlling the ball in the wind is something that comes with lots of experience. Sure, you can take more club and swing less, but doing this requires you to alter swing speed, which is difficult for most golfers.

One thing that any golfer CAN do is understand how different winds affect their distances.

The most important thing to understand is the fact that headwinds affect the golf ball more than tailwinds do. This is simply because a headwind causes more lift, causing the ball to stay in the air longer, while a tailwind causes less lift, forcing the ball downwards towards the ground. The more time the ball is in the air, the more it moves. Pretty simple.

I have created a simple Excel Ball-Flight calculator that you can play around with in your spare time and gauge some of the different wind, temperature, and elevation effects.

Although my calculator is a good baseline estimate of ball flight effects based on Trackman data, I suggest checking out this post from Golf WRX, which explains wind effects in more detail.

Temperature and Coefficient of Restitution

The temperature of the air while playing golf has a significant effect on your golf ball, and tends to increase the carry distance in hot temperatures, and decrease the distance in cool temperatures.

As a competitive golfer, I have played tournaments in temperatures ranging from 35 degrees all the way up to 100 degrees, and neither of the extremes are enjoyable. When playing in the cold, just about every golf shot creates painful vibrations of the golf shaft, while hot temperatures require you to drink a bottle of water every hole. Not only are you dealing with bodily reactions to the extreme temperatures, your golf ball is fighting its own battle.

The calculation for various temperatures is rather simple. We use 70 degrees as the baseline, and add/subtract 1 yard for every 3 degrees of temperature deviation (download the ball-flight effects calculator here).

One thing that this measurement does not cover is the effect that storing your golf balls in a warm place immediately prior to the round has on the golf ball.

It wouldn’t make much sense to cool a ball down for a hot round of golf, so I will focus in on ways we can gain distance. If you are planning on playing golf in cold temperatures, there is a way to increase your carry distance off the tee during this round. Although your body is cold, the ball doesn’t have to be. Rubber is a poor conductor of heat, which means that heat is lost at a slow rate as well. If you store a sleeve of golf balls in the house the night before your round, and then keep them in your pocket during the round, you will not see as drastic of a reduction in total distance.

This is because a warm golf ball has a higher coefficient of restitution than a cold one, meaning the ball will “pop” off the clubface more aggressively when warm. To understand the coefficient of restitution concept, check out the video below:

The coefficient of restitution is an inherent part of each individual golf ball (i.e. a ProV1 is going to have a different coefficient value than a Top Flight), and determines how much energy is converted to internal energy (friction, etc.) through impact. Think about what would happen if you dropped a ball of clay to the ground. With its low coefficient of restitution, the clay will probably not bounce back up at all (inelastic collision). Now think about dropping a golf ball to the ground. Thanks to its high coefficient of restitution, it will bounce almost all the way up to the point it was dropped (elastic collision).

So storing your golf balls indoors before a cold round will help increase the distance of your shots, but inevitably, the golf balls will cool down throughout the round. To some (including me), this seems disadvantageous, because the carry distances of your clubs is constantly changing throughout the round. I would rather hit my irons 10 yards less and be consistent than nut a pitching wedge 145 yards on hole 1 and only 130 on hole 18.

Elevation Effects

Finally, we have reached the last ball-flight factor!

Although most golfers can estimate elevation effects fairly well with the naked eye, I believe it is still worth covering.

The calculation is simple. For every 1 yard of elevation differential between your ball and the target, you must play 1 yard up or downhill.

The only factor that is not commonly recognized is the elevation of the town/city you are playing golf in. In most locations, this effect is negligent, but if you are playing in the mountains of Utah or Colorado, you must adjust accordingly. A great way to find this information about a golf course is via Google Earth. I have created a short tutorial that walks you through this process.

Conclusion

Several thousand words later, and we have covered all of the ball-flight effects. I hope this post alongside my post about the “new ball-flight” effects was helpful!

Many of these effects may seem out of your control as a golfer, but by understanding them, you will have a much better idea how to control your golf ball. After all, that’s the name of the game isn’t it?